Linear vs. Exponential Functions - Algebra I & Functions Review

These flashcards cover essential vocabulary terms and their corresponding definitions related to linear and exponential functions as taught in an Algebra I review.

Linear Function

A function that creates a straight line when graphed, characterized by a constant rate of change.

Exponential Function

A function where a constant base is raised to a variable exponent, resulting in growth or decay by a constant factor.

Exponential Decay

A decrease in a quantity by a fixed percentage over time, often modeled with the form R(t) = P_0 (1 - r)^t.

Half-life

The time required for a quantity to reduce to half its initial value, commonly used in radioactive decay.

Average Rate of Change

The slope of a secant line connecting two points on a function, given by the formula: (f(b) - f(a)) / (b - a).

Piecewise Function

A function composed of multiple sub-functions, each applied to a certain interval of the domain.

Properties of Equality

Rules that allow manipulation of equations while maintaining balance, such as addition, subtraction, multiplication, and division.

Function Evaluation

The process of substituting a given input into a function to obtain an output.

Domain of a Function

The set of all possible input values (x) that a function can accept.

Quadratic Function

A polynomial function of degree two, typically represented as f(x) = ax^2 + bx + c, where the graph forms a parabola.

System of Equations

A set of equations with the same variables, which can be solved together to find the values that satisfy all equations.

Polynomial Expression

An algebraic expression that consists of variables raised to non-negative integer powers and coefficients.